Coordinate rings of some SL₂-character varieties

2022/02/15 by Muñoz, Vicente, Ovejero, Jesús Martín · 1 citation
#14D20 #14M35 #20G05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2202.07227

Abstract

We determine generators of the coordinate ring of SL₂-character varieties. In the case of the free group F₃ we obtain an explicit equation of the SL₂-character variety. For free groups F_k we find transcendental generators. Finally, for the case of the 2-torus, we get an explicit equation of the SL₂-character variety and use the description to compute their E-polynomials.

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